# Math Help - Verifying Identities

1. ## Verifying Identities

Verify that the left side is equal to the right side

$\frac{1+cos 3t}{sin3t} + \frac{sin 3 t}{1+ cos 3 t} = 2 csc 3 t$

2. Originally Posted by purplec16
Verify that the left side is equal to the right side

1+cos 3t/sin3t + sin 3 t/ 1+ cos 3 t = 2 csc 3 t
I can't read this. Please use brackets where they're needed or else use LaTeX.

Is it $\frac{1 + \cos{3t}}{\sin{3t}} + \frac{\sin{3t}}{1 + \cos{3t}} = 2\csc{3t}$?

3. Yes that is the correct reading it would not go through correctly in the latex, sorry, i fixed it

4. $\frac{1 + \cos{3t}}{\sin{3t}} + \frac{\sin{3t}}{1 + \cos{3t}} = \frac{(1 + \cos{3t})^2}{\sin{3t}(1 + \cos{3t})} + \frac{\sin^2{3t}}{\sin{3t}(1 + \cos{3t})}$

$= \frac{1 + 2\cos{3t} + \cos^2{3t} + \sin^2{3t}}{\sin{3t}(1 + \cos{3t})}$

$= \frac{1 + 2\cos{3t} + 1}{\sin{3t}(1 + \cos{3t})}$

$= \frac{2 + 2\cos{3t}}{\sin{3t}(1 + \cos{3t})}$

$= \frac{2(1 + \cos{3t})}{\sin{3t}(1 + \cos{3t})}$

$= \frac{2}{\sin{3t}}$

$= 2\csc{3t}$.

5. Can you help me with another one?

6. Originally Posted by purplec16
Can you help me with another one?
I can if you post it...

7. In this post or another? The next one is: $(sec u- tan u)(csc u + 1)= cot u$

8. Originally Posted by purplec16
In this post or another? The next one is: $(sec u- tan u)(csc u + 1)= cot u$
$(\sec{u} - \tan{u})(\csc{u} + 1) = \sec{u}\csc{u} + \sec{u} - \csc{u}\tan{u} - \tan{u}$

$= \frac{1}{\cos{u}\sin{u}} + \frac{1}{\cos{u}} - \frac{\sin{u}}{\cos{u}\sin{u}} - \frac{\sin{u}}{\cos{u}}$

$= \frac{1 + \sin{u} - \sin{u} - \sin^2{u}}{\cos{u}\sin{u}}$

$= \frac{1 - \sin^2{u}}{\cos{u}\sin{u}}$

$= \frac{\cos^2{u}}{\cos{u}\sin{u}}$

$= \frac{\cos{u}}{\sin{u}}$

$= \cot{u}$.

9. I dont see how you transition from the 2nd line to the the 3rd line

10. Originally Posted by purplec16
I dont see how you transition from the 2nd line to the the 3rd line
Get a common denominator of $\cos{u}\sin{u}$.

11. I get it never mind

12. Originally Posted by purplec16
I understand that part, I dont understand how you got the numerator
$\frac{1}{\cos{u}\sin{u}} + \frac{1}{\cos{u}} - \frac{\sin{u}}{\cos{u}\sin{u}} - \frac{\sin{u}}{\cos{u}}$

$= \frac{1}{\cos{u}\sin{u}} + \frac{\sin{u}}{\cos{u}\sin{u}} - \frac{\sin{u}}{\cos{u}\sin{u}} - \frac{\sin^2{u}}{\cos{u}\sin{u}}$

$= \frac{1 + \sin{u} - \sin{u} - \sin^2{u}}{\cos{u}\sin{u}}
$

13. Thank You so much, I understand

14. Can you help me with one more please?

15. Originally Posted by purplec16
Can you help me with one more please?
Go on... Since I've given you two full solutions though, I'd like to see your attempt at proving it this time...

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